Development of methods to accurately estimate human immunodeficiency virus (HIV) incidence rate remains a challenge. Ideally, one would follow a random sample of HIV-negative individuals under a longitudinal study design and identify incident cases as they arise. Such designs can be prohibitively resource intensive and therefore alternative designs may be preferable. We propose such a simple, less resource-intensive study design and develop a weighted log likelihood approach which simultaneously accounts for selection bias and outcome misclassification error. The design is based on a cross-sectional survey which queries individuals' time since last HIV-negative test, validates their test results with formal documentation whenever possible, and tests all persons who do not have documentation of being HIV-positive. To gain efficiency, we update the weighted log likelihood function with potentially misclassified self-reports from individuals who could not produce documentation of a prior HIV-negative test and investigate large sample properties of validated sub-sample only versus pooled sample estimators through extensive Monte Carlo simulations. We illustrate our method by estimating incidence rate for individuals who tested HIV-negative within 1.5 and 5 years prior to Botswana Combination Prevention Project enrolment. This article establishes that accurate estimates of HIV incidence rate can be obtained from individuals' history of testing in a cross-sectional cohort study design by appropriately accounting for selection bias and misclassification error. Moreover, this approach is notably less resource-intensive compared to longitudinal and laboratory-based methods.

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